Suppose that \(E(\mathbb {Q}_p)[p]\)  is non-trivial, i.e. (REF ) splits.
By applying Gross' tameness criterion [1]}The unchecked compatibility in [1]} is confirmed in the Ph.D. thesis of Bryden Cais [3]}., this is equivalent to that
the image of the restriction of the residual representation to \(\mathrm {Gal}(\overline{\mathbb {Q}}_p/\mathbb {Q}_p)\)  is diagonalizable.
